Related papers: Constrained Cuts, Flows, and Lattice-Linearity
Distributed optimization algorithms are frequently faced with solving sub-problems on disjoint connected parts of a network. Unfortunately, the diameter of these parts can be significantly larger than the diameter of the underlying network,…
A lattice reduction is an algorithm that transforms the given basis of the lattice to another lattice basis such that problems like finding a shortest vector and closest vector become easier to solve. Some of the famous lattice reduction…
The simple cubic lattice defines a set of points at regular distances. The volume of the Voronoi cells around each point may serve as a weight for integration over the entire space. We add interstitial points to this grid according to the…
We present a simple and faster algorithm for computing fair cuts on undirected graphs, a concept introduced in recent work of Li et al. (SODA 2023). Informally, for any parameter $\epsilon>0$, a $(1+\epsilon)$-fair $(s,t)$-cut is an…
We develop a novel distributed algorithm for the minimum cut problem. We primarily aim at solving large sparse problems. Assuming vertices of the graph are partitioned into several regions, the algorithm performs path augmentations inside…
In the last few years the so--called "linear deterministic" model of relay channels has gained popularity as a means of studying the flow of information over wireless communication networks, and this approach generalizes the model of…
Biclustering, also called co-clustering, block clustering, or two-way clustering, involves the simultaneous clustering of both the rows and columns of a data matrix into distinct groups, such that the rows and columns within a group display…
We study the electrical distribution network reconfiguration problem, defined as follows. We are given an undirected graph with a root vertex, demand at each non-root vertex, and resistance on each edge. Then, we want to find a spanning…
We introduce FlowCutter, a novel algorithm to compute a set of edge cuts or node separators that optimize cut size and balance in the Pareto-sense. Our core algorithm solves the balanced connected st-edge-cut problem, where two given nodes…
The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. In this paper, we engineer the fastest known exact algorithm for the problem.…
We generalize the polynomial-time solvability of $k$-\textsc{Diverse Minimum s-t Cuts} (De Berg et al., ISAAC'23) to a wider class of combinatorial problems whose solution sets have a distributive lattice structure. We identify three…
Shortest paths in complex networks play key roles in many applications. Examples include routing packets in a computer network, routing traffic on a transportation network, and inferring semantic distances between concepts on the World Wide…
In this thesis, we present fast deterministic algorithm to find small cuts in distributed networks. Finding small min-cuts for a network is essential for ensuring the quality of service and reliability. Throughout this thesis, we use the…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
For a partially ordered set P, we denote by Co(P) the lattice of order-convex subsets of P. We find three new lattice identities, (S), (U), and (B), such that the following result holds. Theorem. Let L be a lattice. Then L embeds into some…
The Max-Cut problem is a fundamental NP-hard problem, which is attracting attention in the field of quantum computation these days. Regarding the approximation algorithm of the Max-Cut problem, algorithms based on semidefinite programming…
The Multicut problem asks for a minimum cut separating certain pairs of vertices: formally, given a graph $G$ and demand graph $H$ on a set $T\subseteq V(G)$ of terminals, the task is to find a minimum-weight set $C$ of edges of $G$ such…
We present the first near-linear work and poly-logarithmic depth algorithm for computing a minimum cut in a graph, while previous parallel algorithms with poly-logarithmic depth required at least quadratic work in the number of vertices. In…
The prototypical high-dimensional statistics problem entails finding a structured signal in noise. Many of these problems exhibit an intriguing phenomenon: the amount of data needed by all known computationally efficient algorithms far…
A partial algebra construction of Gr\"atzer and Schmidt from "Characterizations of congruence lattices of abstract algebras" (Acta Sci. Math. (Szeged) 24 (1963), 34-59) is adapted to provide an alternative proof to a well-known fact that…